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1 Electronic Supplementary Material (ESI) for New Journal of Chemistry. This journal is The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2019 Electronic Supplementary Information Theoretical characterization of hexagonal 2D Be 3 N 2 monolayer Saif Ullah, a,* Pablo A. Denis, b Rodrigo B. Capaz c, and Fernando Sato a a- Departamento de Física, Instituto de Ciências Exatas, Campus Universitário, Universidade Federal de Juiz de Fora, Juiz de Fora, MG , Brazil b- Computational Nanotechnology, DETEMA, Facultad de Química, UDELAR, CC 1157, Montevideo, Uruguay c- Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, RJ , Brazil * sullah@fisica.ufjf.br capaz@if.ufrj.br Computational details: We make use of four DFT codes i.e. VASP 1, QE 2, 3, SIESTA 4, 5, and Gaussian 6 to predict the theoretical synthesis, stability, and electronic properties of Be 3 N 2 and its derivatives. We use norm-conserving (NC) Troullier-Martins pseudopotentials (PPs) 7 in SIESTA. We use LDA 8, PBE-GGA 9, LDA-PBE hybrid, vdw-df1 10, and vdw-df2-c09 11, 12 as implemented in SIESTA. The hybrid functional is actually not a hybrid in a true sense due to the absence of exact Hartree- Fock exchange. The term hybrid is used as we mixed two different functionals, LDA and PBE versions of GGA. We select % from both these functionals to define the exchange energy while for correlation part, 75% and 25% is used from LDA and GGA, respectively. The orbital confining cut-off is 0.01 Ry and the split-norm is We tested increasing the mesh cut-off to 300 Ry, which gave the same results as that of 200 Ry. For AIMD simulations, we constructed a 4x4 supercell of Be 3 N 2 and performed the heat treatment at 300K, 600K, and 900K. An NVT ensemble with Nosé thermostat is used with a time step of 1 fs. In VASP, the kinetic energy cutoff is 500 ev. Geometry optimization is carried out with two different convergence criteria: 10-6 ev for energy and 0.02 ev/å for forces; and 10-8 ev for energy and ev/å for forces in some cases. Both of these criteria gave converged results. To deal with of partial occupancies,

2 tetrahedron method with Blochl correction 13 is used. For bulk graphite-like layered structures, we use dispersion corrected PBE-D2 14 scheme and for total energy comparison, all the systems are recalculated with the same functional. As for as QE is concerned, we use PPs from PSlibrary 15 and SSSP library 16, 17. The cut-off is selected to be 60 Ry for the expansion of the wavefunctions (wfc) and 8-times of this cut-off is used for charge density. The default 4 wfc is selected if the PPs are NC. A smaller cutoff of 40Ry also produces well-converged results. The convergence criteria of energy (between two electronic steps) and two ionic steps are Ry and 10-7 Ry. The optimization is done until the Hellmann-Feynman forces are less than 10-5 Ry/a.u. For selfconsistent field convergence, we use more strict criteria of Ry. We use Methfessel-Paxton (mp) 18 and Marzari-Vanderbilt (mv) 19 smearing method with Ry and found that mp smearing method with a broadening of 0.01 Ry is a wise choice in term of accuracy versus computational speed. Phonons spectra are calculated by DFPT method using the Phonon code, which is a part of PWscf package. We use PBE, PBE-sol, and NC PPs and found that all the levels employed gave the same results. In phonon calculations, the convergence criterium is selected to be Ry. Furthermore, vdw-df1, rev-vdw-df2 20, vdw-df2-c09 (with C-09 exchange), rvv10 21, 22 schemes are also used in QE. All the calculations are performed with spin polarization to investigate possible magnetism. We also tested the inclusion of spin-orbit-coupling (SOC) in our calculations but no effect was noted on the electronic band structure or the total energy of Be3N2. Furthermore, we also tested antiferromagnetic calculations with various configurations. After checking all these possibilities, we can safely say that Be3N2 is a non-magnetic direct band-gap semiconductor. DFT Code Lattice Lattice Be-N Cohesive energy Formation level parameter parameter bond (ev/atom) energy a=b (Å) c (Å) lengths (ev) (Å) β-be 3 N 2 PBE SIESTA vdw- DF/DZP SIESTA

3 PBE a QE PBE-sol QE paw-pbe QE rvv10 QE vdw-df1 QE vdw-df2 QE rev-vdw- QE DF2 vdw- QE DF2-C09 2D Be 3 N 2 LDA SIESTA PBE SIESTA Hybrid SIESTA vdw- SIESTA DF/DZP PBE-NC QE PBE-sol QE PBE a QE vdw-df1 QE rvv10 QE rev-vdw- QE DF2 vdw- QE DF2-C09 paw-lda QE LDA-NC QE Table S1: Structural properties of β-be 3 N 2 and monolayer Be 3 N 2 are shown at the different level of theories.

4 DFT level Exfoliation Energy (ev/å 2 ) vdw-df/dzp vdw-df1 rvv10 DF2-C rev-vdw-df2 Table S2: The Exfoliation energies for monolayer Be 3 N 2 at various vdw-df levels are shown. Fig. S1: The geometric structure of bulk β-be 3 N 2 calculated at PBE-sol level of theory is depicted. DFT level Code Band-gap (ev) LDA SIESTA 2.78 PBE SIESTA 2.86 Hybrid SIESTA 2.76 vdw-df/dzp SIESTA 2.76 vdw-df/dzp-soc SIESTA 2.76 PBE QE 2.82

5 PBE-sol QE 2.77 HSEH1PBE Gaussian 4.10 Table S3: Calculated band-gaps of monolayer Be3N2 at various levels of theory. Fig. S2: Alkali atoms (Li, Na, and K) adsorbed within the hollow site (a) top view (b) side view and on the top of hollow site (c) top view (d) side view) on monolayer Be 3 N 2. In the latter case, the height of Li, Na, and K from the plane of monolayer Be 3 N 2 is found to be Å, Å, and Å, respectively. Branch Frequency (THz) Infrared (I)-Active Raman-R-Active depol-fact

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